Integrability versus separability for the multi-centre metrics
High Energy Physics - Theory
2009-11-10 v1
Abstract
The multi-centre metrics are a family of euclidean solutions of the empty space Einstein equations with self-dual curvature. For this full class, we determine which metrics do exhibit an extra conserved quantity quadratic in the momenta, induced by a Killing-St\" ackel tensor. Our systematic approach brings to light a subclass of metrics which correspond to new classically integrable dynamical systems. Within this subclass we analyze on the one hand the separation of coordinates in the Hamilton-Jacobi equation and on the other hand the construction of some new Killing-Yano tensors.
Cite
@article{arxiv.hep-th/0309207,
title = {Integrability versus separability for the multi-centre metrics},
author = {Galliano Valent},
journal= {arXiv preprint arXiv:hep-th/0309207},
year = {2009}
}
Comments
24 pages, latex, no figure